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Optimal Deterministic Broadcasting in Known Topology Radio Networks

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Abstract

We consider deterministic broadcasting in radio networks whose nodes have full topological information about the network. The aim is to design a polynomial algorithm, which, given a graph G with source s, produces a fast broadcast scheme in the radio network represented by G. The problem of finding a fastest broadcast scheme for a given graph is NP-hard, hence it is only possible to get an approximation algorithm. We give a deterministic polynomial algorithm which produces a broadcast scheme of length \(\mathcal{O}(D + \log ^2 n)\), for every n-node graph of diameter D, thus improving a result of Gąsieniec et al. (PODC 2005) [17] and solving a problem stated there. Unless the inclusion NP \(\subseteq\) BPTIME(\(n^{\mathcal{O}(\log \log n)})\) holds, the length \(\mathcal{O}(D + \log ^2 n)\) of a polynomially constructible deterministic broadcast scheme is optimal.

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Authors and Affiliations

  1. Department of Computer Science, The University of Liverpool, Liverpool, L69 7ZF, UK

    Dariusz R. Kowalski

  2. Département d’informatique, Université du Québec en Outaouais, Gatineau, Québec, J8X 3X7, Canada

    Andrzej Pelc

Authors
  1. Dariusz R. Kowalski
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  2. Andrzej Pelc
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Corresponding author

Correspondence to Dariusz R. Kowalski.

Additional information

A preliminary version of this paper (with a weaker result) appeared in the Proc. 7th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems (APPROX’2004), August 2004, Harvard University, Cambridge, USA, LNCS 3122, 171–182. Research of the second author supported in part by NSERC discovery grant and by the Research Chair in Distributed Computing of the Université du Québec en Outaouais. Part of this work was done during the second author’s visit at the Max-Planck-Institut für Informatik.

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Kowalski, D.R., Pelc, A. Optimal Deterministic Broadcasting in Known Topology Radio Networks. Distrib. Comput. 19, 185–195 (2007). https://doi.org/10.1007/s00446-006-0007-8

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  • DOI: https://doi.org/10.1007/s00446-006-0007-8

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